arXiv:2505.17203v2 Announce Type: replace-cross
Abstract: We study contextual dynamic pricing when a target market can leverage K auxiliary markets — offline logs or concurrent streams — whose mean utilities differ by a structured preference shift. We propose Cross-Market Transfer Dynamic Pricing (CM-TDP), the first algorithm that provably handles such model-shift transfer and delivers minimax-optimal regret for both linear and non-parametric utility models.
For linear utilities of dimension d, where the difference between source- and target-task coefficients is $s_{0}$-sparse, CM-TDP attains regret $tilde{O}((d*K^{-1}+s_{0})log T)$. For nonlinear demand residing in a reproducing kernel Hilbert space with effective dimension $alpha$, complexity $beta$ and task-similarity parameter $H$, the regret becomes $tilde{O}!(K^{-2alphabeta/(2alphabeta+1)}T^{1/(2alphabeta+1)} + H^{2/(2alpha+1)}T^{1/(2alpha+1)})$, matching information-theoretic lower bounds up to logarithmic factors. The RKHS bound is the first of its kind for transfer pricing and is of independent interest.
Extensive simulations show up to 50% lower cumulative regret and 5 times faster learning relative to single-market pricing baselines. By bridging transfer learning, robust aggregation, and revenue optimization, CM-TDP moves toward pricing systems that transfer faster, price smarter.